 
Summary: The Distribution of the Maximum of a Gaussian
Process: Rice Method Revisited.
JeanMarc Aza¨is
, azais@cict.fr
Mario Wschebor
, wscheb@fcien.edu.uy
December 21, 2000
Abstract
This paper deals with the problem of obtaining methods to compute the
distribution of the maximum of a oneparameter stochastic process on a fixed
interval, mainly in the Gaussian case. The main point is the relationship
between the values of the maximum and crossings of the paths, via the so
called Rice's formulae for the factorial moments of crossings.
We prove that for some general classes of Gaussian process the socalled
"Rice series" is convergent and can be used for to compute the distribution
of the maximum. It turns out that the formulae are adapted to the numerical
computation of this distribution and becomes more efficient than other nu
merical methods, namely simulation of the paths or standard bounds on the
tails of the distribution.
We have included some relevant numerical examples to illustrate the power
